Possible to fix a broken shape key with a copy of the model?
Copying shape keys doesn't work because they measure a difference of location from a basis, so your mesh should already know which is that basis location. 

You can try selecting in edit mode the eye edgeloop, then with Ctrl++ expand the selection a certain amount of times (as needed, but count them), P to separate the selection. 

Do the same with the other mesh, then swap and Join (Ctrl+J) the meshes, remove doubles and adjust where necessary.

If this method doesn't work I think you need a little Python script to copy location only, of selected vertices from one object to another.

Consider also the idea of starting from the correct mesh and copying all other vertex data from the textured one (Shift+Ctrl+T for vertices/edges/faces infos; select target, shift select source, Ctrl+L "transfer UV map").